Armando Domiciano de Souza

Fast ray-tracing algorithm for circumstellar structures (FRACS) I. Algorithm description and parameter-space study for mid-IR interferometry of B(e) stars

The physical interpretation of spectro-interferometric data is strongly model-dependent. On one hand, models involving elaborate radiative transfer solvers are too time consuming in general to perform an automatic fitting procedure and derive astrophysical quantities and their related errors. On the other hand, using simple geometrical models does not give sufficient insights into the physics of the object. We propose to stand in between these two extreme approaches by using a physical but still simple parameterised model for the object under consideration. Based on this philosophy, we developed a numerical tool optimised for mid-infrared (mid-IR) interferometry, the fast ray-tracing algorithm for circumstellar structures (FRACS) which can be used as a stand-alone model, or as an aid for a more advanced physical description or even for elaborating observation strategies. FRACS is based on the ray-tracing technique without scattering, but supplemented with the use of quadtree meshes and the full symmetries of the axisymmetrical problem to significantly decrease the necessary computing time to obtain e.g. monochromatic images and visibilities. We applied FRACS in a theoretical study of the dusty circumstellar environments (CSEs) of B[e] supergiants (sgB[e]) in order to determine which information (physical parameters) can be retrieved from present mid-IR interferometry (flux and visibility). From a set of selected dusty CSE models typical of sgB[e] stars we show that together with the geometrical parameters (position angle, inclination, inner radius), the temperature structure (inner dust temperature and gradient) can be well constrained by the mid-IR data alone. Our results also indicate that the determination of the parameters characterising the CSE density structure is more challenging but, in some cases, upper limits as well as correlations on the parameters characterising the mass loss can be obtained. Good constraints for the sgB[e] central continuum emission (central star and inner gas emissions) can be obtained whenever its contribution to the total mid-IR flux is only as high as a few percents. Ray-tracing parameterised models such as FRACS are thus well adapted to prepare and/or interpret long wavelengths (from mid-IR to radio) observations at present (e.g. VLTI/MIDI) and near-future (e.g. VLTI/MATISSE, ALMA) interferometers.

Interferometric-Doppler imaging of stellar surface abundances

Similarly as the technique of Doppler Imaging from spectroscopic observations, Differential Interferometry makes it possible to measure the disturbances of photocentroid location of an unresolved star as a function of wavelength and to deduce the corresponding stellar map. We show the imaging potential of a tomographic technique which combines time-resolved spectroscopy and long baseline interferometry, providing information that cannot be obtained otherwise with each of these techniques taken at once. In particular, here we consider the example of mapping abundance inhomogeneities, performing numerical experiments with realistic spectral resolutions and signal-to-noise ratios expected for operating (VLTI, GI2T) or close-to-operating long baseline interferometers (Chara, Keck). We show that the accurate maps of stellar surface abundance distribution can be obtained using regularized inversion by Maximum Entropy method. The technique is also applicable to other classes of stellar surface imaging as magnetic field and temperature spots but within the classical instrumental context (without polarimetric device) it can hardly discriminate among different distributions. We discuss the importance of Spectro-Polarimetric Interferometry observations (Rousselet-Perraut et al., this proceedings) in order to discriminate and simultaneously map abundance/temperature inhomogeneities and magnetic fields of chemically peculiar (CP) stars.

VLTI-AMBER observations of Eta Carinae with high spatial resolution and spectral resolutions of 1,500 and 10,000

We present the first interferometric NIR observations of the LBV η Carinae with high spectral resolution. The observations were carried out with three 8.2 m VLTI Unit Telescopes in the K-band. The raw data are spectrally dispersed interferograms obtained with spectral resolutions of 1,500 (MR-K mode) and 12,000 (HR-K mode). The observations were performed in the wavelength range around both the He I 2.059 μm and the Brγ 2.166 μm emission lines. The spectrally dispersed AMBER interferograms allow the investigation of the wavelength dependence of the visibility, differential phase, and closure phase of η Car. In the K-band continuum, a diameter of 4.0±0.2 mas (Gaussian FWHM) was measured for η Cars optically thick wind region, whereas the Brγ and He I emission line regions are larger. If we fit Hillier et al. model visibilities to the observed AMBER visibilities, we obtain 50% encircled-energy diameters of 4.3, 6.5 and 9.6 mas in the 2.17 μm continuum, the He I, and the Brγemission lines, respectively. In the continuum near the Brγ line, an elongation along a position angle of 128° ± 15° was found, consistent with previous VLTI/VINCI measurements. We find good agreement between the measured visibilities and the predictions of the radiative transfer model of Hillier et al. For the interpretation of the non-zero differential and closure phases measured within the Brγ line, we present a simple geometric model of an inclined, latitude-dependent wind zone. Our observations support theoretical models of anisotropic winds from fast-rotating, luminous hot stars with enhanced high-velocity mass loss near the polar regions.

Interferometric Surface Mapping of Rapidly Rotating Stars: Application to the Be star Achernar

Rotation is one of the fundamental parameters that governs the physical structure and evolution of stars. Massive stars are those presenting the highest rotation velocities and thus those for which the consequences of rotation are the strongest. On the stellar photosphere fast-rotation induces (1) a geometrical flattening and (2) a non-uniform distribution of flux/effective temperature (gravity darkening effect). A detailed mapping of these effects on the stellar photosphere, including large scale surface velocity fields, is nowadays possible thanks to modern techniques of optical/infrared long-baseline interferometry (OLBI). In this paper we focus on the measurement of gravity darkening from OLBI, while the determination of flattening is detailed by Kervella (this volume). In addition, we also show that, for fast-rotators, the combination of OLBI and spectroscopy (spectro-interferometry) allows to go beyond the spatial resolution limit of interferometers in order to measure angular sizes of stars, otherwise not measurable by classical OLBI techniques. The results presented here are based on ESO-VLTI interferometric observations of the Be star Achernar.

The photosphere and circumstellar environment of the Be star Achernar

Achernar is a key target to investigate high stellar rotation and the Be phenonemon. It is also the hottest star for which detailed photospheric information is available. Here we report our results to determine the photospheric parameters of Achernar and evaluate how the emission of a Viscous Decretion Disk (VDD) around it would be observable. The analysis is based on interferometric data (PIONIER and AMBER at ESO-VLTI), complemented by spectroscopy and polarimetry for the circumstellar emission. For the first time fundamental parameters of a Be photosphere were determined. The presence of a residual disk at the quiescent phase and some characteristics of the new formed disk (2013 activity) are also discussed. This is rare opportunity to precisely determine the stellar brightness distribution and evaluate the evolution of a just formed Be disk.

Hα spectropolarimetry of GG Car

We present spectropolarimetric observations of the B[e] supergiant star GG Car at two epochs. Polarization line effects along Hα are analysed using the Q–U diagram. In particular, the polarization position angle (PA) obtained using the line effect allows to constrain the symmetry axis of the disk/envelope. The depolarization line effect around Hα is evident in the Q–U diagram for both epochs, confirming that light from the system is intrinsically polarized. A rotation of the PA along Hα is also observed, indicating a counter-clockwise rotating disk. The intrinsic PA calculated using the line effect (∼85◦) is consistent between our two epochs, suggesting a clearly defined symmetry axis of the disk.

FRACS: modelling of the dust disc of the B[e] CPD-57° 2874 from VLTI/MIDI data

The physical interpretation of spectro-interferometric data is strongly model dependent. On one hand, models involving elaborate radiative transfer solvers are in general too time consuming to perform an automatic fitting procedure and derive astrophysical quantities and their related errors. On the other hand, using simple geometrical models does not give sufficient insights into the physics of the object. We developed a numerical tool optimised for mid-infrared (mid-IR) interferometry, the Fast Ray-tracing Algorithm for Circumstellar Structures (FRACS). Thanks to the short computing time required by FRACS, best-fit parameters and uncertainties for several physical quantities were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, disc inclination.

Spectroscopic and interferometric approach for differential rotation in massive fast rotators

The coupling between the convective region in the envelope and rotation can produce a surface latitudinal differential rotation that may induce changes of the stellar geometry and on the spectral line profiles that it may be scrutinized spectroscopically and by interferometry.